Question

Q) A car starting from rest accelerated at a rate of 0.5 m/s 2 up to two kilometres. What would be
the final velocity of the car and how much time would it take to cover 1.6 km?
Q) A car is travelling at 72 km/he for a distance of 0.2 km, after which its velocity became 90
km/hr. Calculate its acceleration.

Answer 1

Answer:

First convert the velocity to m/s from km/h. Here, you get it as 20 m/s.

Now, you have final velocity: v = 0 m/s as the body is going to come at rest.

Whole initial velocity: u = 20m/s,

The acceleration is retarding in nature

So, you have a = (-2 m/s²)

Using the Kinematic Equation : v=u+at you get t = 2s

And using v²=u²+2as

You have s=v²/2as = 400/(2)(2),

i.e. s = 100 m

Answer 2

Answer:

Explanation:

Answer 1.

Given :-

Initial velocity, u = 0 (As car starts from rest)

Acceleration, a = 0.5 m/s²

Distance covered, s = 1.6 km = 1.6 × 1000 = 1600 m

To Find :-

Final velocity, v = ??

Formula to be used :-

1st and 2nd equation of motion,

i.e, v = u + at and s = ut + 1/2 × at²

Solution :-

Putting all the values, we get

s = ut + 1/2 × at²

⇒ 1600 = 0 × t + 1/2 × 0.5 × t²

⇒ 1600 = 5/20 × t²

⇒ t² = 1600 × 20/5

⇒ t² = 6400

⇒ t = 80 seconds

Now, final velocity

v = u + at

⇒ v = 0 + 0.5 × 80

⇒ v = 40 m/s

Hence, the  final velocity is 40 m/s.

Answer 2.

Given :-

Initial velocity, u = 72 km/h = 72 × 5/18 = 20 m/s

Final velocity, v = 90 km/h = 90 × 5/18 = 25 m/s

Distance covered, s = 0.2 km = 0.2 × 1000 = 200 m

To Find :-

Acceleration, a = ??

Formula to be used :-

1st and 3rd equation of motion,

i.e, v = u + at and v² - u² = 2as

Solution :-

Putting the values, we get

v² - u² = 2as

⇒ (25)² - (20)² = 2 × a × 200

⇒ 625 - 400 = 400a

⇒ 225 = 400a

⇒ 225/400 = a

⇒ a = 0.5625 m/s²

Hence, the acceleration is 0.5625 m/s².